Spectral numbers and manifolds with boundary

Abstract

We consider a smooth submanifold N with a smooth boundary in an ambient closed manifold M and assign a spectral invariant c(α, H) to every singular homological class α ∈ H∗(N) and a Hamiltonian H defined on the cotangent bundle T∗ M. We also derive certain properties of spectral numbers, for example we prove that spectral invariants c± (H, N) associated to the whole Floer homology HF∗(H, N: M) of the submanifold N, are the limits of decreasing nested family of open sets.